Answer: The value of x is ![\frac{50}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B50%7D%7B3%7D)
Step-by-step explanation:
Let the original price of gasoline be y
Since we have given that
Price of gasoline rose by 20% during January fell by 20% during February rose by 25% in March and fell by x% in April.
So, According to question,
In January, Price became
![\frac{100+20}{100}\times y=\frac{120}{100}\times y=\frac{6}{5}\times y=\frac{6y}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B100%2B20%7D%7B100%7D%5Ctimes%20y%3D%5Cfrac%7B120%7D%7B100%7D%5Ctimes%20y%3D%5Cfrac%7B6%7D%7B5%7D%5Ctimes%20y%3D%5Cfrac%7B6y%7D%7B5%7D)
Similarly, In February, Price became
![\frac{100-20}{100}\times \frac{6y}{5}=\frac{80}{100}\times \frac{6y}{5}=\frac{4}{5}\times \frac{6y}{5}=\frac{4}{5}\times \frac{6y}{5}=\frac{24y}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B100-20%7D%7B100%7D%5Ctimes%20%5Cfrac%7B6y%7D%7B5%7D%3D%5Cfrac%7B80%7D%7B100%7D%5Ctimes%20%5Cfrac%7B6y%7D%7B5%7D%3D%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B6y%7D%7B5%7D%3D%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B6y%7D%7B5%7D%3D%5Cfrac%7B24y%7D%7B25%7D)
Similarly, in March, Price became,
![\frac{100+25}{100}\times \frac{4\times 6y}{25}=\frac{125}{100}\times \frac{6\times 4y}{25}=\frac{5}{4}\times \frac{24y}{25}=\frac{5}{4}\times \frac{24y}{25}=\frac{6y}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B100%2B25%7D%7B100%7D%5Ctimes%20%5Cfrac%7B4%5Ctimes%206y%7D%7B25%7D%3D%5Cfrac%7B125%7D%7B100%7D%5Ctimes%20%5Cfrac%7B6%5Ctimes%204y%7D%7B25%7D%3D%5Cfrac%7B5%7D%7B4%7D%5Ctimes%20%5Cfrac%7B24y%7D%7B25%7D%3D%5Cfrac%7B5%7D%7B4%7D%5Ctimes%20%5Cfrac%7B24y%7D%7B25%7D%3D%5Cfrac%7B6y%7D%7B5%7D)
similarly, in April , Price became,
![\frac{100-x}{100}\times \frac{6y}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B100-x%7D%7B100%7D%5Ctimes%20%5Cfrac%7B6y%7D%7B5%7D)
so, we have given that the price of gasoline at the end of April was the same as it had been at the beginning of January.
So, it becomes,
![\frac{6y}{5}\times \frac{100-x}{100}=y\\\\6(100-x)=500\\\\600-6x=500\\\\600-500=6x\\\\100=6x\\\\x=\frac{100}{6}=\frac{50}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B6y%7D%7B5%7D%5Ctimes%20%5Cfrac%7B100-x%7D%7B100%7D%3Dy%5C%5C%5C%5C6%28100-x%29%3D500%5C%5C%5C%5C600-6x%3D500%5C%5C%5C%5C600-500%3D6x%5C%5C%5C%5C100%3D6x%5C%5C%5C%5Cx%3D%5Cfrac%7B100%7D%7B6%7D%3D%5Cfrac%7B50%7D%7B3%7D)
Hence, the value of x is ![\frac{50}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B50%7D%7B3%7D)